ITS simple brother
Of course it is simple.
Paul didn't thesalonians confused, think the rapture already happen.
You are swapping out the phrase "the Day of the Lord" and having it say "Rapture" instead, to have it [incorrectly] say,
"[purporting] that the Rapture IS PRESENT [PERFECT indicative - G1764 Strong's Greek: 1764. ἐνίστημι (enistémi) -- to place in, to be at hand, perf. part. to be present (biblehub.com) ]"...
...they were under NO SUCH DELUSION!!
Instead, the actual wording (as your original post was worded), "[purporting] that THE DAY OF THE LORD IS PRESENT [PERFECT indicative - G1764]]"
"The Day of the Lord" is "an EARTHLY-located-TIME-PERIOD-[of much duration]-involving-JUDGMENTs-unfolding-upon-the-earth, followed-by-a-period-of-time-of-BLESSINGs" (NOT "a singular 24-hr day"), which STARTS [/ARRIVES] at the INITIAL "birth PANG [SINGULAR; 1Th5:2-3; Matt24:4/Mk13:5]" that Jesus spoke of in His Olivet Discourse (where "the beginning of birth PANGS [PLURAL]" is EQUIVALENT to the "SEALS" of Rev6 at the START of the trib... THAT is the ARRIVAL of "the DOTL TIME-PERIOD" to play out upon the earth, over TIME).
The "definition" of that phrase is NOT "Rapture". ["Rapture [IN THE AIR]"]
No one was "[purporting] that the RAPTURE *is present [perfect indicative - G1764]*" (your incorrect interp of v.2).
Than Paul say, that day Will not happen before the antichrist Being reveal.
The text of verse 3 is not saying that, it says (instead),
"that day [the DOTL from v.2!] will not be present if not shall have come THE DEPARTURE *FIRST* and [distinctly] the man of sin be revealed..."
notice... ONE THING *FIRST* (not BOTH of those things FIRST), which distinguishes them.
Once "the man of sin" is REVEALED, the "DOTL" WILL BE PRESENT (to unfold upon the earth; JUDGMENTs unfolding upon the earth over the course of SOME TIME... "IN HIS TIME" [re: "the man of sin" and ALL he will DO over the course of THOSE SEVEN YEARS])
And we know antichrist reveal during second part of gt.
Nope. At "SEAL #1" (the INITIAL "birth PANG [SINGULAR; 1Th5:2-3 (DOTL's *ARRIVAL*), Matt24:4/Mk13:5 at the START of the trib, NOT its MIDDLE! (i.e. Dan9:27A[26B="whose COMING"2Th2:9a])])
So rapture after gt.
...if you MIS-define words, ignore grammar, disregard corresponding passages from Scripture (comparing Scripture with Scripture), and think that the Thessalonians were total buffoons who would be so easily "persuaded" to think "Rapture" had happened, when they could EASILY LOOK AROUND THEM to see the PLAIN-AS-DAY *EVIDENCE* (IF that were the claim--but it WAS NOT!!) They would have NO NEED for Paul to write them such a letter (which would have, in itself, taken MUCH TIME to get to them!)
What WAS "persuasive" (to what they were ACTUALLY being told by false-conveyors) was "that THE DAY OF THE LORD *IS PRESENT* [PERFECT indicative]": an EARTHLY time-period consisting of JUDGMENTs unfolding upon the earth OVER THE COURSE of some TIME.
THAT would be EASY (and would be PERFECTLY REASONABLE) for them to be [wrongly] persuaded to believe, BECAUSE of the VERY NEGATIVE THINGS they were presently and ONGOINGLY *experiencing* (per 2Th1:4).
The other makes no sense whatsoever. ZERO PEOPLE had DISAPPEARED!
The text does not SAY what you are having it to say.
[study all that the OT has to say about "the DOTL"--it is not a mere "singular 24-hr day" nor does it COMMENCE at the moment of Christ's "RETURN," but quite a bit EARLIER THAN THAT